I tried to import into Thunderbird the contacts.vcf as exported from GMail, but birthdays didn't make it into Thunderbird's address book, although vCard's field
BDAY:yyyymmdd is present. Could someone please post a working example?
A workaround is to sync contacts using a Thunderbird Add-On as answered in How to import google contacts into Ubuntu 13.04?
Another offline (offline is desired in this question) workaround could be to convert Google's vCard export into Thunderbird's import format LDIF. As opposed to vCard the birthday in ldif is not one field but three (birthyear, birthmonth, birthday).